Motion Graphs for Character Animation

Motion Graphs for Character Animation 

Parag Chaudhuri 

Indian Institute of Technology Bombay 

Research Promotion Workshop on 

Introduction to Graph and Geometric Algorithms 

Thapar University 

Patiala 

October 30, 2010 

Motion Graphs for Character Animation

Outline 

Introduction 

The Need for Motion Data 

Using Motion Data 

Character and Motion Data 

Character Representation 

Motion Representation 

Motion Graphs 

Idea 

Construction 

Generating Motion 

More Motion Graphs 

Conclusions 



Character animation is about movement. 

c○ Aardman Animations, Nintendo Co., Ltd. 



Creating plausible movement requires a lot of skill and time. 

Source: Sintel, The Durian Open Movie Project 



How difficult can it be - it is only one character... 



...then imagine a thousand or a million! 

c○ Walden Media, Rhythm and Hues Studios, Massive Software 



Capture movement of performers and use it in animation. 

c○ James Cameron, 20th Century Fox, Vicon, Ubisoft 



Problems 

◮ Captured data can be voluminous. 

◮ Processing data motion data is intensive. 

◮ Capturing all possible motion is impossible. 

◮ Motion Capture is expensive and cumbersome. 

Solutions 

◮ Organize and represent data. 

◮ Combine data intelligently to synthesize new motion. 

◮ Simulate physics to dynamically generate new motion. 



Problems 

◮ Captured data can be voluminous. 

◮ Processing data motion data is intensive. 

◮ Capturing all possible motion is impossible. 

◮ Motion Capture is expensive and cumbersome. 

Solutions 

◮ Organize and represent data. 

◮ Combine data intelligently to synthesize new motion. 

◮ Simulate physics to dynamically generate new motion. 


Outline 

Introduction 







Idea 

Construction 



Conclusions 



A layered representation for the character 

Source: Model courtesy MIRALab 



A set of joints with fixed degrees of freedom... 




...joined with rigid links or bones form the skeleton of the character. 




This forms a rooted tree of rigid transformations. 




Layered on top of this is a triangle mesh of the character’s skin. 




When the skeleton moves, the skin moves along. 




Motion data is typically captured in the form of joint trajectories 

Source: Vicon IQ 



Motion data is typically captured in the form of joint trajectories 



It is stored in one of many standard formats 


Outline 

Introduction 







Idea 

Construction 



Conclusions 


Idea 

Every motion clip is a graph. Vertex ∼ pose, Edge ∼ transition frames. 


Idea 

There are many such clips in a motion database. 


Idea 

Find similar poses between clips. Add transitions between them. 


Idea 

Find similar poses between clips. Add transitions between them. 


Idea 

Now any walk on this graph... 


Idea 

...generates a new, smooth motion. 


Construction 

Similarity between poses across clips 

A simple distance measure between joints is a bad idea as some 

joints have more influence on the pose and they may also be 

subject to constraints. 

A pose is defined only up to a rigid coordinate transformation. 

Hence comparing two pose requires identifying compatible 

coordinate systems. 

A seamless transition must account not only for differences in body 

posture, but also in joint velocities, accelerations, and possibly 

higher-order derivatives. 


Construction 












Construction 












Construction 

D(P i , P j ) = min 

θ,x o,z o 

n∑ 

ω k ‖pi k − T θ,xo,zo pj k ‖ 2 

k=1 

Compute the distance 

metric over a window of 

2L + 1 frames centered 

at P i and P j . 

Constructing Good Quality Motion Graphs for Realistic Human Animation, Limin Zhaog, PhD Thesis, University of 

Pennsylvania, 2009. 

Motion Graphs, Lucas Kovar, Michael Gleicher and Frédéric Pighin, SIGGRAPH 2002 


Construction 

Create transitions 

between frames for 

which similarity satisfies 

a threshold. 

Linear interpolations of 

translations, Spherical 

linear interpolations for 

rotations. 

Prune the graph for 

dead ends. Retain only 

the largest strongly 

connected component. 




Random walks on the motion graph are not interesting 

So we search for motion that satisfies some objective 

Minimize a function f (w) such that 

n∑ 

f (w) = f ([e 1 , · · · e n ]) = g([e 1 , · · · e i−1 ] , e i ) 

- where f (w) gives the total path error for a path w = [e 1 , · · · e n ] on 

the graph 

i=1 

- g(w, e) is a scalar function that gives the additional error when the 

edge e is added to an existing path w. 

- In addition to this we also have a halting criteria. 



Path Synthesis - making the character move on a path given by the user 

g(w, e) = 

n∑ 

‖Q ′ (s(w, e i ) − Q(s(w, e i )‖ 2 

i=1 




Motion Styles 



Outline 

Introduction 







Idea 

Construction 



Conclusions 


Motion from Annotations 

Annotate the motions, paint a time line, search 

Motion Synthesis from Annotations, Okan Arikan, David Forsyth, James O’Brien, SIGGRAPH 2003 


Motion Patches 

Motion capture motion in patches, graph between patches 

Motion Patches: Building Blocks for Virtual Environments Annotated with Motion Data, Kang Hoon Lee, Myung Geol Choi 

and Jehee Lee, SIGGRAPH 2006 


Dynamic Response 

Motion capture motion in patches, graph between patches 

Dynamic Response for Motion Capture Animation, Victor Zordan, Anna Majkowska, Bill Chiu and Matthew Fast, 

SIGGRAPH 2005 


Self Adaptive Animation 

Transitions driven by camera position 

Self Adaptive Animation based on User Perspective, Parag Chaudhuri, George Papagiannakis, Nadia Magnenat-Thalmann, 

CGI 2008 


Outline 

Introduction 







Idea 

Construction 



Conclusions 


Conclusions 

Motion Graphs are very useful in character animation. 

Extensively used for real-time animation synthesis. 

Cutting edge research area in Computer Graphics. 

Future going toward a combination of physics simulation and 

motion capture. 


Thank You

Motion Graphs for Character Animation

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